How does the core sit inside the mantle?

Amin Coja-Oghlan; Oliver Cooley; Mihyun Kang; Kathrin Skubch

How does the core sit inside the mantle?

Combinatorics 2015-04-01 v1 Discrete Mathematics Probability

Authors: Amin Coja-Oghlan , Oliver Cooley , Mihyun Kang , Kathrin Skubch

Abstract

The $k$ -core, defined as the largest subgraph of minimum degree $k$ , of the random graph $G(n,p)$ has been studied extensively. In a landmark paper Pittel, Wormald and Spencer [JCTB 67 (1996) 111--151] determined the threshold $d_k$ for the appearance of an extensive $k$ -core. Here we derive a multi-type Galton-Watson branching process that describes precisely how the $k$ -core is embedded into the random graph for any $k\geq3$ and any fixed average degree $d=np>d_k$ . This generalises prior results on, e.g., the internal structure of the $k$ -core.

Keywords

random graphs graph theory

Cite

@article{arxiv.1503.09030,
  title  = {How does the core sit inside the mantle?},
  author = {Amin Coja-Oghlan and Oliver Cooley and Mihyun Kang and Kathrin Skubch},
  journal= {arXiv preprint arXiv:1503.09030},
  year   = {2015}
}

How does the core sit inside the mantle?

Abstract

Keywords

Cite

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